To prove the existence of such a locking configuration, the strategy is to use the convex duality technique from the theory of convex program See [1]}, [2]}, [3]} for a physicist-friendly introduction to the technical details on this topic. to prove the existence of a feasible multiflow such that
\(\sum \limits _{i < j} {2\int _i {{{\vec{v}}_{ij}}} } \ge \sum \limits _i {{S_i}}. \) 
